On projectional resolution of identity on the duals of certain Banach spaces
1987 ◽
Vol 35
(3)
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pp. 363-371
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Keyword(s):
A consequence of the main proposition includes results of Tacon, and John and Zizler and says: If a Banach space X possesses a continuous Gâteaux differentiable function with bounded nonempty support and with norm-weak continuous derivative, then its dual X* admits a projectional resolution of the identity and a continuous linear one-to-one mapping into c0 (Γ). The proof is easy and selfcontained and does not use any complicated geometrical lemma. If the space X is in addition weakly countably determined, then X* has an equivalent dual locally uniformly rotund norm. It is also shown that l∞ admits no continuous Gâteaux differentiable function with bounded nonempty support.
1974 ◽
Vol 11
(2)
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pp. 161-166
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Keyword(s):
1983 ◽
Vol 26
(2)
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pp. 163-167
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Keyword(s):
2020 ◽
Vol 1664
(1)
◽
pp. 012038
1981 ◽
Vol 89
(1)
◽
pp. 129-133
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1990 ◽
Vol 108
(3)
◽
pp. 523-526
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Keyword(s):
1988 ◽
Vol 30
(2)
◽
pp. 145-153
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